From Glauber dynamics to Metropolis algorithm: Smaller delay in optimal CSMA

Abstract

Glauber dynamics, a method of sampling a given probability distribution via a Markov chain, has recently made considerable contribution to the MAC scheduling research, providing a tool to solve a long-standing open issue - achieving throughput-optimality with light message passing under CSMA. In this paper, we propose a way of reducing delay by studying generalized Glauber dynamics parameterized by βϵ[0, 1], ranging from Glauber dynamics (β=0) to the Metropolis algorithm (β =1). The same stationary distribution is sustained across this generalization, thus maintaining the long-term optimality. However, a different choice of β results in a significantly different second-order behavior (or variability) that has large impact on delay, which is hardly captured by the recent research focusing on delay in the large n (the number of nodes) asymptotic. We formally study such second-order behavior and its resulting delay performance, and show that larger β achieves smaller delay. Our results provide new insight into how to operate CSMA for large throughput and small delay in real, finite-sized systems.